Electroencephalography (EEG) is a commonly used clinical approach for the diagnosis of epilepsy which is a life-threatening neurological disorder. Many algorithms have been proposed for the automatic detection of epileptic seizures using traditional machine learning and deep learning. Although deep learning methods have achieved great success in many fields, their performance in EEG analysis and classification is still limited mainly due to the relatively small sizes of available datasets. In this paper, we propose an automatic method for the detection of epileptic seizures based on deep metric learning which is a novel strategy tackling the few-shot problem by mitigating the demand for massive data. First, two one-dimensional convolutional embedding modules are proposed as a deep feature extractor, for single-channel and multichannel EEG signals respectively. Then, a deep metric learning model is detailed along with a stage-wise training strategy. Experiments are conducted on the publicly-available Bonn University dataset which is a benchmark dataset, and the CHB-MIT dataset which is larger and more realistic. Impressive averaged accuracy of 98.60% and specificity of 100% are achieved on the most difficult classification of interictal (subset D) vs ictal (subset E) of the Bonn dataset. On the CHB-MIT dataset, an averaged accuracy of 86.68% and specificity of 93.71% are reached. With the proposed method, automatic and accurate detection of seizures can be performed in real time, and the heavy burden of neurologists can be effectively reduced.